EE 205 Dr. Chokri. Belhaj Ahmed
Electric Circuits II
Balanced Three Phase Circuits
Lecture # 01
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EE 205 Dr. Chokri. Belhaj Ahmed
Objective of this lecture is as follows:
o Introduction of three-phase circuit concept
o Balance Three Phase Voltages.
o Positive Sequence Voltages
o Negative Sequence Voltages
After finishing this lecture, you should be able to:
¾ Identify the main components of three-phase circuit.
¾ Understand the role of each main components of three-phase circuit.
¾ Differentiate between the balanced voltages phases
¾ Imagine the positive and negative sequence voltages opposite direction.
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EE 205 Dr. Chokri. Belhaj Ahmed
Introduction of three-phase circuit concept
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The three-phase circuit is the main circuit structure used in power system.
The electrical power generation is accomplished through three-phase circuit.
The three phase connection lines transmit power over long distance.
The energy is distributed and consumed at the load level through three phase and single phase
Generating, Transmitting, Distributing and consuming electric power is achieved through the three
phase circuit
The basic structure of a three phase system consists of voltage source, transformers, transmission
line and connected loads
Figure 1.Three phase Circuit Components
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EE 205 Dr. Chokri. Belhaj Ahmed
Balance Three Phase Voltages
• Three sinusoidal voltages form a set of balanced voltages when they have the same amplitudes and
frequency.
• These voltages are shifted in phase by 120o with each other.
• The standard practice is to name those phases by a, b and c and use phase a as reference.
• These voltages represent phase a voltage, phase b voltage and phase c voltage.
Figure 2. Phase Voltages of Balance Three Phase source.
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EE 205 Dr. Chokri. Belhaj Ahmed
Figure 3. Phasor Diagram for Balance Three Phase Voltages
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EE 205 Dr. Chokri. Belhaj Ahmed
Positive Sequence Voltages
• When phase b voltage lags the reference phase a voltage by 120o and consequently phase c
voltage must lead phase a voltage by 120o.
• The above relation between phases is known as positive sequence or abc.
Figure 4. Phasor Diagram of Balance Three Phase Voltages (abc) sequence
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EE 205 Dr. Chokri. Belhaj Ahmed
• In phasor notation we represent the set of balanced positive sequence voltage as:
V a =V ∠00
Vb =V ∠−1200
Vc =V ∠+120
0
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EE 205 Dr. Chokri. Belhaj Ahmed
Negative Sequence Voltages
• When phase b voltage leads the reference phase a voltage by 120o and consequently phase c
voltage must lag phase a voltage by 120o.
• The above relation between phases is known as negative sequence or acb.
Figure 5. Phasor Diagram of Balance Three Phase Voltages (acb) sequence
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EE 205 Dr. Chokri. Belhaj Ahmed
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In phasor notation we represent the set of balanced negaitive sequence voltage as:
V
a
=V ∠ 00
V b =V ∠ + 1200
V c =V ∠−1200
• An important Characteristic of a positive or negative sequence set of balanced voltages is that the
sum the phasor voltages is equal to zero
V a +V b +V c = 0
• As a consequence the sum the related instantaneous voltages is equal to zero
υa + υb + υc = 0
• If the phase sequence is known and one of the voltages of the balanced set is known then the entire
set becomes known.
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EE 205 Dr. Chokri. Belhaj Ahmed
Example:
¾ Define the phase sequence for this first set voltages
υa = 208 cos(ωt + 27o )V .
υb = 208cos(ωt + 147o )V .
υc = 208 cos(ωt − 93o ) V .
¾ The relevant phsors are :
Va = 208∠27 V .
0
¾ Therefore the sequence is
Vb = 208∠ +1470V .
V c = 208∠− 930V .
acb
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EE 205 Dr. Chokri. Belhaj Ahmed
¾ Define the phase sequence for this second set voltages
υa = 4160 cos(ωt −18o )V .
υb = 4160 cos(ωt −138o )V .
υc = 4160 cos(ωt +102o ) V .
¾ The relevant phsors are :
0
V a = 4160∠ −180V . Vb = 4160∠−1380V . Vc = 4160∠+102 V .
¾ Therefore the sequence is
abc
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EE 205 Dr. Chokri. Belhaj Ahmed
Self Test:
Which options are true for a set of three sinusoidal balanced voltages?
a) Three sinusoidal voltages have the same amplitudes and different frequency.
b) Two sinusoidal voltages are shifted in phase by 120o from the reference voltage
c) The three voltages are shifted in phase by 120o with each other
d) In a positive sequence phase b is lagging on phase a by 240o.
e) In a negative sequence phase b is leading on phase a by 120o .
answer: c, and e
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